Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.IsMultiplicative
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropA morphism property is multiplicative if it contains identities and is stable by composition.
- Cited by
- 332 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by440
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.Over.pullbackstatement and proof · cited by 42
- HomotopicalAlgebra.ReedyStructurestatement · cited by 30
- CategoryTheory.MorphismProperty.Comma.forgetstatement and proof · cited by 28
- CategoryTheory.MorphismProperty.Comma.mapLeftstatement and proof · cited by 28
- CategoryTheory.MorphismProperty.Comma.mapRightstatement and proof · cited by 28
- CategoryTheory.MorphismProperty.Over.mapstatement and proof · cited by 26
- CategoryTheory.WideSubcategorystatement · cited by 26
- CategoryTheory.WideSubcategory.objstatement and proof · cited by 22
- HomotopicalAlgebra.ReedyStructure.degstatement and proof · cited by 19
- CategoryTheory.InducedWideCategory.Hom.homstatement and proof · cited by 19
- CategoryTheory.MorphismProperty.Comma.mapRightIsostatement and proof · cited by 18
- CategoryTheory.MorphismProperty.Comma.mapLeftIsostatement and proof · cited by 18
Showing the 200 most cited of 440.